Concept of Synthetic Division

2009-08-19 1:07 am
Take a example,

Use synthetic division to divide 2x^3-3x^2+4x-1 by 2x+1.


2x^3-3x^2+4x-1

=(2x^2-4x+6)(x+1/2)- 4

=(x^2-2x+3)(2x+1)- 4 <---點解(x+1/2)會變返(2x+1)?背後原因&Step 係咩??

thanks
更新1:

(x+1/2)會變返(2x+1)...係因為想將個divisor變返(2x+1)定係因為唔accept分數,所以通分母??

回答 (1)

2009-08-19 1:24 am
✔ 最佳答案
2x^2 - 4x + 6 = 2(x^2 - 2x + 3)
(x + 1/2) = (2x + 1)/2
so multiplying the two together, we get
2(x^2 - 2x + 3)(2x + 1)/2 = (x^2 - 2x + 3)(2x + 1)



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